In short: the question is, does the length of the path affect the outcome of detecting a photon?
Consider the single photon beam splitter experiment. Does the probability of detecting the photon change if the distance between the detectors is unequal? Because light has a fixed velocity c. If the photon is detected at a place that is nearer (detection means absorption unless some special means are used), then it can no longer be anywhere else.
This might be the case in Wheeler's delayed choice experiment: http://www.sciencenews.org/pictures/112010/essay_delayed_zoom.gif As the particle detection path is shorter when that path is chosen, the photon will always be detected there?
If so, could temperature gradient on the detection plate cause unequal expansion of the plate on quantum scales affecting the outcome of detecting photon because the place where they reach on the plate first is different?